{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:UBMX4KPR4LDG7OFLOQF2WGO7O6","short_pith_number":"pith:UBMX4KPR","schema_version":"1.0","canonical_sha256":"a0597e29f1e2c66fb8ab740bab19df77995beb19fd21e7a101190eddb2572a26","source":{"kind":"arxiv","id":"1506.02447","version":1},"attestation_state":"computed","paper":{"title":"Inaudibility of sixth order curvature invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Dorothee Schueth, Teresa Arias-Marco","submitted_at":"2015-06-08T11:38:26Z","abstract_excerpt":"It is known that the spectrum of the Laplace operator on functions of a closed Riemannian manifold does not determine the integrals of the individual fourth order curvature invariants $\\operatorname{scal}^2$, $|\\operatorname{ric}|^2$, $|R|^2$, which appear as summands in the second heat invariant $a_2$. We study the analogous question for the integrals of the sixth order curvature invariants appearing as summands in $a_3$. Our result is that none of them is determined individually by the spectrum, which can be shown using various examples. In particular, we prove that two isospectral nilmanifo"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1506.02447","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-06-08T11:38:26Z","cross_cats_sorted":[],"title_canon_sha256":"8698dfe47f77a6061df9fedc7be13f167c62a76d9325da6265632f00520de544","abstract_canon_sha256":"a053f929e7123487801ff81a9a6ff700e7662a819de89c47ae34be015c2e2554"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:39.779402Z","signature_b64":"LHhpQeDig6eT6zIJEqPNeV/uNCOd0WT4HbDsz4WmVRvNNjUzy6XucoDT9/WzNIKk79CSIFG0RKNiAw/6GDKwCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0597e29f1e2c66fb8ab740bab19df77995beb19fd21e7a101190eddb2572a26","last_reissued_at":"2026-05-18T00:42:39.778716Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:39.778716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inaudibility of sixth order curvature invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Dorothee Schueth, Teresa Arias-Marco","submitted_at":"2015-06-08T11:38:26Z","abstract_excerpt":"It is known that the spectrum of the Laplace operator on functions of a closed Riemannian manifold does not determine the integrals of the individual fourth order curvature invariants $\\operatorname{scal}^2$, $|\\operatorname{ric}|^2$, $|R|^2$, which appear as summands in the second heat invariant $a_2$. We study the analogous question for the integrals of the sixth order curvature invariants appearing as summands in $a_3$. Our result is that none of them is determined individually by the spectrum, which can be shown using various examples. In particular, we prove that two isospectral nilmanifo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02447","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1506.02447","created_at":"2026-05-18T00:42:39.778813+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.02447v1","created_at":"2026-05-18T00:42:39.778813+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02447","created_at":"2026-05-18T00:42:39.778813+00:00"},{"alias_kind":"pith_short_12","alias_value":"UBMX4KPR4LDG","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"UBMX4KPR4LDG7OFL","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"UBMX4KPR","created_at":"2026-05-18T12:29:44.643036+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UBMX4KPR4LDG7OFLOQF2WGO7O6","json":"https://pith.science/pith/UBMX4KPR4LDG7OFLOQF2WGO7O6.json","graph_json":"https://pith.science/api/pith-number/UBMX4KPR4LDG7OFLOQF2WGO7O6/graph.json","events_json":"https://pith.science/api/pith-number/UBMX4KPR4LDG7OFLOQF2WGO7O6/events.json","paper":"https://pith.science/paper/UBMX4KPR"},"agent_actions":{"view_html":"https://pith.science/pith/UBMX4KPR4LDG7OFLOQF2WGO7O6","download_json":"https://pith.science/pith/UBMX4KPR4LDG7OFLOQF2WGO7O6.json","view_paper":"https://pith.science/paper/UBMX4KPR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.02447&json=true","fetch_graph":"https://pith.science/api/pith-number/UBMX4KPR4LDG7OFLOQF2WGO7O6/graph.json","fetch_events":"https://pith.science/api/pith-number/UBMX4KPR4LDG7OFLOQF2WGO7O6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UBMX4KPR4LDG7OFLOQF2WGO7O6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UBMX4KPR4LDG7OFLOQF2WGO7O6/action/storage_attestation","attest_author":"https://pith.science/pith/UBMX4KPR4LDG7OFLOQF2WGO7O6/action/author_attestation","sign_citation":"https://pith.science/pith/UBMX4KPR4LDG7OFLOQF2WGO7O6/action/citation_signature","submit_replication":"https://pith.science/pith/UBMX4KPR4LDG7OFLOQF2WGO7O6/action/replication_record"}},"created_at":"2026-05-18T00:42:39.778813+00:00","updated_at":"2026-05-18T00:42:39.778813+00:00"}